### Strain Hardening Simulation on CPU

We can run a tensile test simulation of a single-crystal Cu using the following commands (running ExaDiS on CPU).  This type of simulation is also called the strain-hardening simulation because it predicts stress-strain curves in the plastic regime where the flow stress increases with strain.

```bash
cd ${OPENDIS_DIR}
cd examples/10_strain_hardening/
export OMP_NUM_THREADS=8
python3 test_strain_hardening_exadis.py
```

#### Initial Condition

The initial dislocation configuration for this simulation is read from a data file ```180chains_16.10e.data``` (in ParaDiS data format) by the following Python commands
```bash
G = ExaDisNet()
G.read_paradis('180chains_16.10e.data')
```
The simulation cell size is 15 𝜇m × 15 𝜇m × 15 𝜇m, subjected to periodic boundary conditions in all three directions. The initial dislocation density is 𝜌<sub>0</sub> ≈ 1.2 × 10<sup>12</sup> m<sup>-2</sup>.  The initial dislocation structure can be visualized by [Ovito](https://www.ovito.org/) as shown below.  The dislocation lines are colored according to the dislocation character angle.
```{figure} initial_configuration_Ovito.png
:alt: Screenshot of the final configuration
:width: 552px
```
Click [here](./Ovito_settings.png) to see the Ovito settings used to generate the plot above.


#### Simulation Setup

Many simulation parameters are specified in the dictionary variable ```state```.  The ```sim``` objects contains all the information, including the sub-modules of the simulation.  In particular, ```max_strain``` specifies the maximum strain to be reached in the simulation (here running up to 0.01 = 1% strain).  The following line in the Python program executes the simulation
```bash
sim.run(net, state)
```

#### Simulation Behavior
The simulation creates a folder called ```output_fcc_Cu_15um_1e3``` to store the results files.  On MC3.stanford.edu (with 8 OMP threads), it takes about 12 minutes to run the first 100 steps of the simulation.

To specify a different stopping criterion, we can modify the constructor for ```sim```, e.g. by switching from ```max_strain=0.01``` to ```max_step=1600``` to run the simulation for 1600 time steps.  The simulation takes about 21 hours on MC3.stanford.edu (with 8 OMP threads) to complete. The simulation will write a data file to the output folder for every 100 steps.  The [stress_strain_dens_1600_CPU.dat](./stress_strain_dens_1600_CPU.dat) file stores certain essential information of the tensile test --- here it contains 5 columns corresponding to step, strain, stress (Pa), dislocation density (m<sup>-2</sup>) and wall-clock time (sec), respectively.

The final dislocation configuration (config.1600.data) after 1600 steps is shown below.
```{figure} CPU_final_configuration_Ovito.png
:alt: Screenshot of the final configuration
:width: 552px
```

The predicted stress-strain curve is shown below.
```{figure} Stress_strain_CPU.png
:alt: stress-strain curve
:width: 352px
```

Here is how the total dislocation density changes with strain.  The increase of dislocation density (i.e. dislocation multiplication) with strain is a key mechanism for strain-hardening.
```{figure} Density_strain_CPU.png
:alt: dislocation density-strain curve
:width: 352px
```

#### Restart Simulation
The simulation produces a set of restart files in the output directory.  We can restart the simulation from any of these restart files.  For example,
```bash
cd ${OPENDIS_DIR}
cd examples/10_strain_hardening/
export OMP_NUM_THREADS=8
python3 test_strain_hardening_exadis.py 100
```
would restart the simulation from the file ```output_fcc_Cu_15um_1e3/restart.100.exadis```.